By Igor V. Andrianov, Jan Awrejcewicz, Leonid I. Manevitch
In this publication a close and systematic therapy of asymptotic equipment within the idea of plates and shells is gifted. the most positive factors of the e-book are the elemental ideas of asymptotics and its functions, conventional ways comparable to typical and singular perturbations, in addition to new ways akin to the composite equations strategy. The booklet introduces the reader to the sector of asymptotic simplification of the issues of the speculation of plates and shells and may be priceless as a instruction manual of equipment of asymptotic integration. delivering a state of the art overview of asymptotic functions, this e-book might be precious as an creation to the sector for rookies in addition to a reference e-book for specialists.
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Additional info for Asymptotical Mechanics of Thin-Walled Structures
Looking for the saddle point we get: h'(z) = -1- Z2, ZI,2 = ±i, h(ZI,2) = =+=~i, h"(ZI,2) = =+=2i. Level of the surface p in both points is lower of the input maximum. 5. Maximum of p on the new contour is achieved in the passage points, and each of these points introduces a contribution to the main asymptotics term. 39) (second one is found if one of contour radius is taken in direction arg w = 0). In this case t > 0 the saddle point z = 1 is accounted, and it yields exponentially increasing asymptotics.
The surface p(x,y) becomes more complex. 35) yields the problem of its analytical continuation in the domain of contour deformation and a question of overcoming of possible singularities occur. Parameter t can be complex, and the asymptotic is constructed for It I ~ 00 in a certain sector arg t. Finally, contour of integration may depend on t. In general case, the main difficulty of the saddlepoint method application is focused on a proof of observation that in the point z 0 the function p possesses not only local, but also global maximum for whole chosen integration contour.
494 m. 3 ~ Fig. 3. An estimation of accuracy of the perturbation method. 36). 25. 5%. 3 Stability of the cantilever beam In the stability theory the Ishlinskii-Leibenzon method is widely used to analyse constructions with free edges [353, 424]. The idea is focused on that the in the equilibrium equations the parametric terms are neglected keeping them only in the boundary conditions. The problem of the physical motivation of those simplifications is still under considerations in the literature.
Asymptotical Mechanics of Thin-Walled Structures by Igor V. Andrianov, Jan Awrejcewicz, Leonid I. Manevitch